Stacy is a high school Calculus teacher. She assigns 45 problems for homework. There are twice as many multiple choice problems as free response, and 7 more free response than true/false. How many true/false questions are there?

Let x represent the number of true/false questions

Free response:x+7

Multiple choice: 2(x+7)=2x+14

Total:x+x+7+2x+14=45

4x+21=45

4x=24

x=

<<6=6>>6 true/false questions #### 6 I bought a TV for $1700 excluding tax. What is the price of the television when calculating 15% of the value-added tax? The value-added tax is 1700*15% = <<1700*15*.01=255>>255. The price of the television including tax 1700+255 = $<<1700+255=1955>>1955. #### 1955 A merchant bought 15 keyboards and 25 printers for a total of $2050. If a keyboard costs $20, how much does a printer cost? 15 keyboards at $20 per keyboard cost a total of 15*$20=$<<15*20=300>>300 The total cost of printers and keyboards is $2050 so 25 printers cost $2050-$300=$<<2050-300=1750>>1750 1 printer cost $1750/25=$<<1750/25=70>>70 #### 70 Frank is walking through a corn maze. He has already spent 45 minutes inside. He has done 4 other corn mazes and finished those in 50 minutes on average. How much longer can he spend inside if he wants to ensure that his average doesn't go above 60 minutes per maze? He needs to keep his total time at 300 or below because 5 x 60 = <<5*60=300>>300 His total time spent in the other mazes is 200 because 4 x 50 = <<4*50=200>>200 His total time spent in the five mazes thus far is 245 because 200 + 45 = <<200+45=245>>245 He can spend 55 more minutes on this maze before his average go above 60 because 300 - 245 = <<300-245=55>>55 #### 55 A train travels 270 miles in 3 hours. At the same rate, how many additional hours would it take to travel an additional 180 miles? The rate is 270/3=<<270/3=90>>90 mph. Then it takes an additional 180/90=<<180/90=2>>2 hours. #### 2 Marcus can fit 5 pies in his oven at once. He bakes 7 batches of pies, then slips and drops 8 of them. How many pies are left? First find the total number of pies Marcus bakes: 5 pies/batch * 7 batches = <<5*7=35>>35 pies Then subtract the number of pies Marcus drops: 35 pies - 8 pies = <<35-8=27>>27 pies #### 27 James and Lisa ordered 2 small pizzas. Each pizza has 6 slices. James ate 2/3 of all the slices. How many slices of pizza did James eat? There are a total of 2 * 6 = <<2*6=12>>12 slices of pizza. Since James ate 2/3 of all the slices, he ate 2/3 * 12 = <<2/3*12=8>>8 slices of pizza. #### 8 Carlos and Diego are racing around the block. Carlos runs around the entire block in 3 minutes. Diego runs around half the block in 2.5 minutes and then is tripped by a dog and can't finish. Assuming he kept up the same speed the entire race, what would've been the average time in seconds for the racers? If he finished the race, it would've taken 5 minutes because 2.5 x 2 = <<2.5*2=5>>5 Their total time would've been 8 minutes because 3 + 5 = <<3+5=8>>8 The average would've been 4 minutes because 8 / 2 = <<8/2=4>>4 The average time in seconds would've been 240 because 4 x 60 = <<4*60=240>>240 #### 240 If Ruby is 2 centimeters shorter than Pablo. Pablo is 70 centimeters taller than Charlene. Janet is 62 centimeters tall and Charlene is twice that tall. How tall is Ruby? Charlene is 2 * 62 cm = <<2*62=124>>124 cm tall. Pablo is 70 cm + 124 cm = <<70+124=194>>194 cm tall. Ruby is 194 cm - 2 = <<194-2=192>>192 cm tall. #### 192 A party of 4 order 3 dozen oysters on the half shell for $15.00 a dozen, 2 pounds of steamed shrimp for $14.00 a pound and 2 pounds of fried clams for $13.50 a pound. If they split the bill equally, how much will they each owe? They ordered 3 dozen oysters at $15.00 a dozen so that's 3*15 = $<<3*15=45.00>>45.00 They ordered 2 pounds of shrimp for $14.00 a pound so that's 2*14 = $<<2*14=28.00>>28.00 They ordered 2 pounds of fried clams for $13.50 a pound so that's 2*13.50 = $<<2*13.50=27.00>>27.00 All total their bill comes to 45+28+27 = $<<45+28+27=100.00>>100.00 Their bill was $100.00 and they are splitting it equally amongst 4 people so they each owe 100/4 = $<<100/4=25.00>>25.00 #### 25